Recursive and nonextendible functions over the reals; filter foundation for recursive analysis. II

In this paper we continue our work of Kalantari and Welch (1998). There we introduced machinery to produce a point-free approach to points and functio ns on topological spaces and found conditions for both which lend themselve s to effectivization. While we studied recursive points in that paper, here , we present two useful classes of recursive functions on topological space s, apply them to the reals, and find precise accounting for the nature of t he properties of some examples that exist in the literature. We end with a construction of a recursive function on a small subset of the unit interval which is strongly nonextendible. (C) 1999 Elsevier Science B.V. All rights reserved.